ODE
\[ x^4 y''''(x)+6 x^3 y'''(x)+9 x^2 y''(x)+3 x y'(x)+y(x)=0 \] ODE Classification
[[_high_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.160564 (sec), leaf count = 30
\[\{\{y(x)\to (c_2 \log (x)+c_1) \cos (\log (x))+(c_4 \log (x)+c_3) \sin (\log (x))\}\}\]
Maple ✓
cpu = 0.009 (sec), leaf count = 29
\[[y \left (x \right ) = \sin \left (\ln \left (x \right )\right ) \textit {\_C1} +\textit {\_C2} \cos \left (\ln \left (x \right )\right )+\textit {\_C3} \sin \left (\ln \left (x \right )\right ) \ln \left (x \right )+\textit {\_C4} \cos \left (\ln \left (x \right )\right ) \ln \left (x \right )]\] Mathematica raw input
DSolve[y[x] + 3*x*y'[x] + 9*x^2*y''[x] + 6*x^3*y'''[x] + x^4*y''''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> Cos[Log[x]]*(C[1] + C[2]*Log[x]) + (C[3] + C[4]*Log[x])*Sin[Log[x]]}}
Maple raw input
dsolve(x^4*diff(diff(diff(diff(y(x),x),x),x),x)+6*x^3*diff(diff(diff(y(x),x),x),x)+9*x^2*diff(diff(y(x),x),x)+3*x*diff(y(x),x)+y(x) = 0, y(x))
Maple raw output
[y(x) = sin(ln(x))*_C1+_C2*cos(ln(x))+_C3*sin(ln(x))*ln(x)+_C4*cos(ln(x))*ln(x)]